Melbourne Housing Market-Paper1
Intro Data Science
Team 2
2021-03-28
1 Introduction
This paper discusses our project using data on housing prices in Melbourne in 2017. The establishment of a real estate price prediction system is a key task for the healthy development of the current real estate industry. Having a simple predictive and inferential method to model housing prices helps commerce determine fair prices and allows governments to determine property taxes. This project aims to learn how different factors may affect home sales price by building linear models. Although data that will be utilized was collected in Melbourne, Australia in 2017, the concept that location and home attributes correlate with housing prices could reasonably apply broadly and internationally.
The following questions are the main subjects which this project focuses on:
- Understand if housing prices in Melbourne, Australia can be predicted using this dataset.
- Determine what variables have the greatest impact on housing price.
- Analyze the impacts of location, seller, and construction attributes of homes on the housing market in Melbourne, Australia.
1.1 The Melbourne Housing Snapshot Dataset
- Home Sales in 2017
- Location
- Construction
- Sale
- Location
- Variables: 21
- Numeric: 12
- Categorical: 9
1.2 The Variables
Rooms: Number of rooms
Price: Price (AUS$)
Method: Method of sale - 5 categories
Type: House, Unit, Townhouse - 3 categories
SellerG: Real Estate Agent - 268 categories
Date: Date sold
Distance: Distance from Central Business District
Regionname: Region name - 8 categories
Propertycount: Number of properties that exist in the suburb
Bedroom2 : Number of Bedrooms
Bathroom: Number of Bathrooms
Car: Number of carspots
Landsize: Land Size
BuildingArea: Building Size
YearBuilt: Year home built
CouncilArea: Governing council for the area - 34 categories
Lattitude, Longtitude: GPS location
Suburb: Suburb name - 314 categories
1.3 Goals
- Understand which attributes of a home and its sale determine final sale price
- Attempt to build a reasonable model for inference and/or prediction for final sale price
2 Exploratory Data Analysis (EDA)
The following are excerpts and graphs from our exploratory data analysis. This part of the project familiarizes the reader with our dataset’s attributes as well as lays the foundation for the variables will include in our linear model. The results of our EDA will also inform the future direction of the project.
2.1 Select Data Pairs
2.2 Corrleations
2.3 Map of Melbourne Sales
2.4 Selling Price
2.4.1 Summary of Price Statistics
Mean: $1,075,684
SD: 639310.724
| data.full$Price | |
|---|---|
| Min | 85000 |
| Q1 | 650000 |
| Median | 903000 |
| Mean | 1075684 |
| Q3 | 1330000 |
| Max | 9000000 |
2.4.2 Selling Price Distribution
2.4.3 Log Selling Price Distribution
2.4.4 Price by Region
2.4.5 Price by Number of Rooms (<10 Rooms)
2.4.6 Price by Type of Home
2.5 Test of Independence (Pearson \(\chi^2\)) by Group: Type, Rooms, Regionname, SellerG
\(H_0\): All means equal by group
All reject \(H_0\) with p-value\(<2\times 10^{-16}\)
2.6 Price by Region and Type
3 Linear Modelling
3.1 First Attempt at Linear Model
3.2 Linear Model 2: Removed the Variable with Highest VIF
3.2.1 Model Coefficients
3.3 Linear Model 3: Considered Interactions
3.4 Linear Model 4: Removed Land Size
3.4.1 Model 4 Coefficients
3.4.2 Residual Analysis
3.4.2.1 Normality
3.4.2.2 Influence
3.4.3 Remove Influence Points
3.5 Transformation of Selling Price
3.5.1 Transformed Data - Homogeneity
3.5.2 Transformed Data - Normality
4 Proposed Model
| Observations | 4955 (4548 missing obs. deleted) |
| Dependent variable | Price |
| Type | OLS linear regression |
| F(15,4939) | 425.77 |
| R² | 0.56 |
| Adj. R² | 0.56 |
| Est. | S.E. | t val. | p | |
|---|---|---|---|---|
| (Intercept) | -129445309.64 | 17287919.00 | -7.49 | 0.00 |
| Rooms | 255713.04 | 9273.23 | 27.58 | 0.00 |
| Distance | -44501.15 | 1467.41 | -30.33 | 0.00 |
| Bathroom | 115532.73 | 11453.40 | 10.09 | 0.00 |
| Car | 45801.33 | 7532.08 | 6.08 | 0.00 |
| BuildingArea | 1794.92 | 90.67 | 19.80 | 0.00 |
| Lattitude | -757249.47 | 124821.36 | -6.07 | 0.00 |
| Longtitude | 696894.60 | 116542.04 | 5.98 | 0.00 |
| Propertycount | -3.69 | 1.52 | -2.42 | 0.02 |
| factor(Regionname)Eastern Victoria | 188304.28 | 103229.34 | 1.82 | 0.07 |
| factor(Regionname)Northern Metropolitan | -55889.99 | 30219.79 | -1.85 | 0.06 |
| factor(Regionname)Northern Victoria | 598550.10 | 116506.82 | 5.14 | 0.00 |
| factor(Regionname)South-Eastern Metropolitan | 169831.25 | 51506.18 | 3.30 | 0.00 |
| factor(Regionname)Southern Metropolitan | 212777.72 | 27309.69 | 7.79 | 0.00 |
| factor(Regionname)Western Metropolitan | -86943.29 | 38731.01 | -2.24 | 0.02 |
| factor(Regionname)Western Victoria | 515064.40 | 135131.01 | 3.81 | 0.00 |
| Standard errors: OLS |
4.1 Testing \(R^2\)
\[ \begin{equation} R^2 = 1- \dfrac{RSS}{TSS} \end{equation}=0.441\]
5 Conclusion
5.1 Future Work
- Further explore log transformation
- Consider GLM with log link
- What to do about factors with many levels (100’s)?
- Missing data
- Improve Prediction